899 research outputs found
Designing colloidal ground state patterns using short-range isotropic interactions
DNA-coated colloids are a popular model system for self-assembly through
tunable interactions. The DNA-encoded linkages between particles theoretically
allow for very high specificity, but generally no directionality or long-range
interactions. We introduce a two-dimensional lattice model for particles of
many different types with short-range isotropic interactions that are pairwise
specific. For this class of models, we address the fundamental question whether
it is possible to reliably design the interactions so that the ground state is
unique and corresponds to a given crystal structure. First, we determine lower
limits for the interaction range between particles, depending on the complexity
of the desired pattern and the underlying lattice. Then, we introduce a
`recipe' for determining the pairwise interactions that exactly satisfies this
minimum criterion, and we show that it is sufficient to uniquely determine the
ground state for a large class of crystal structures. Finally, we verify these
results using Monte Carlo simulations.Comment: 19 pages, 7 figure
A finite-temperature liquid-quasicrystal transition in a lattice model
We consider a tiling model of the two-dimensional square-lattice, where each
site is tiled with one of the sixteen Wang tiles. The ground states of this
model are all quasi-periodic. The systems undergoes a disorder to
quasi-periodicity phase transition at finite temperature. Introducing a proper
order-parameter, we study the system at criticality, and extract the critical
exponents characterizing the transition. The exponents obtained are consistent
with hyper-scaling
Some taste substances are direct activators of G-proteins
Amphiphilic substances may stimulate cellular events through direct activation of G-proteins. The present experiments indicate that several amphiphilic sweeteners and the bitter tastant, quinine, activate transducin and Gi/Go-proteins. Concentrations of taste substances required to activate G-proteins in vitro correlated with those used to elicit taste. These data support the hypothesis that amphiphilic taste substances may elicit taste through direct activation of G-proteins
Graphing and Grafting Graphene: Classifying Finite Topological Defects
The structure of finite-area topological defects in graphene is described in
terms of both the direct honeycomb lattice and its dual triangular lattice.
Such defects are equivalent to cutting out a patch of graphene and replacing it
with a different patch with the same number of dangling bonds. An important
subset of these defects, bound by a closed loop of alternating 5- and
7-membered carbon rings, explains most finite-area topological defects that
have been experimentally observed. Previously unidentified defects seen in
scanning tunneling microscope (STM) images of graphene grown on SiC are
identified as isolated divacancies or divacancy clusters
Hierarchical freezing in a lattice model
A certain two-dimensional lattice model with nearest and next-nearest
neighbor interactions is known to have a limit-periodic ground state. We show
that during a slow quench from the high temperature, disordered phase, the
ground state emerges through an infinite sequence of phase transitions. We
define appropriate order parameters and show that the transitions are related
by renormalizations of the temperature scale. As the temperature is decreased,
sublattices with increasingly large lattice constants become ordered. A rapid
quench results in glass-like state due to kinetic barriers created by
simultaneous freezing on sublattices with different lattice constants.Comment: 6 pages; 5 figures (minor changes, reformatted
Determining All Universal Tilers
A universal tiler is a convex polyhedron whose every cross-section tiles the
plane. In this paper, we introduce a certain slight-rotating operation for
cross-sections of pentahedra. Based on a selected initial cross-section and by
applying the slight-rotating operation suitably, we prove that a convex
polyhedron is a universal tiler if and only if it is a tetrahedron or a
triangular prism.Comment: 18 pages, 12 figure
Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
We study the ground-state properties of the spin-half Heisenberg
antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact
diagonalization and a variational mean-field approach. We find evidence that
the star lattice is (besides the \kagome lattice) a second candidate among the
11 uniform Archimedean lattices where quantum fluctuations in combination with
frustration lead to a quantum paramagnetic ground state. Although the classical
ground state of the Heisenberg antiferromagnet on the star exhibits a huge
non-trivial degeneracy like on the \kagome lattice, its quantum ground state is
most likely dimerized with a gap to all excitations. Finally, we find several
candidates for plateaux in the magnetization curve as well as a macroscopic
magnetization jump to saturation due to independent localized magnon states.Comment: new extended version (6 pages, 6 figures) as published in Physical
Review
On the number of simple arrangements of five double pseudolines
We describe an incremental algorithm to enumerate the isomorphism classes of
double pseudoline arrangements. The correction of our algorithm is based on the
connectedness under mutations of the spaces of one-extensions of double
pseudoline arrangements, proved in this paper. Counting results derived from an
implementation of our algorithm are also reported.Comment: 24 pages, 16 figures, 6 table
The Ammann-Beenker tilings revisited
This paper introduces two tiles whose tilings form a one-parameter family of
tilings which can all be seen as digitization of two-dimensional planes in the
four-dimensional Euclidean space. This family contains the Ammann-Beenker
tilings as the solution of a simple optimization problem.Comment: 7 pages, 4 figure
Colourings of lattices and coincidence site lattices
The relationship between the coincidence indices of a lattice and
a sublattice of is examined via the colouring of
that is obtained by assigning a unique colour to each coset of
. In addition, the idea of colour symmetry, originally defined for
symmetries of lattices, is extended to coincidence isometries of lattices. An
example involving the Ammann-Beenker tiling is provided to illustrate the
results in the quasicrystal setting.Comment: 9 pages, 6 figure
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